I cannot access GPT-5 but was able to use gpt-5-nano. It doesn't work correctly -- first, it's not fast; second, I only get response for the first query, and nothing for all subsequent queries. Need to look deeper into it, so will close this PR.

[UPDATE] When using the OpenAI gpt-5 or gpt-5-mini endpoints, I receive explicit errors about "no permission to access endpoint for streaming". Although the gpt-5-nano endpoint doesn't throw the error, I think it's not working due to the same reason.
I will add gpt-5 to the list of supported models for now. Once I have access to gpt-5 model, I can better test it.